A novel shear deformation theory for static analysis of functionally graded plates

A new generalized 5-variable shear deformation theory is proposed to calculate the static response of functionally graded plates. A small exponential function with a shape parameter m is multiplied to a classical trigonometric shear strain shape function to make more accurate distribution of the transverse shear strain in the thickness direction of the functionally graded plates. The novelty of this work is that the shear strain function with the shape parameter m is assumed to vary with power-law indexes. Golden section search is used to determine the values of the optimal shape parameter mop. The present shear strain shape function satisfies the stress free condition at top and bottom surfaces without using any transverse shear correction factors. The governing equations and boundary conditions are derived from the Hamilton principle, and the closed form solutions of Navier-type under simply supported boundary conditions are obtained. The accuracy of the proposed theory is verified by comparing the results of numerical examples with the other existing 2D and quasi-3D solutions. The effect of gradient index, side-to-thickness ratio and aspect ratio on the static response is also studied.